ESTIMATING HOT NUMBERS AND TESTING UNIFORMITY FOR THE LOTTERY

• 成果类型: Article
• 署名作者: JOHNSON, R; KLOTZ, J
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290349
• 发表日期: 1993
• 页码: 662-668
• 关键词: maximum

摘要

We consider the problem of estimating probabilities for the different numbers in a lottery when the winning numbers are selected sequentially without replacement. Numerical methods are developed to compute maximum likelihood estimates of the probabilities and their variance-covariance matrix based on observed outcomes. The generalized likelihood ratio statistic -2 ln(lambda) for testing equiprobable numbers is also given. The methods are applied to a data set from the Lotto America lottery. The properties of the procedure are studied by simulation.